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Approximation in Morrey spaces
Publication . Almeida, Alexandre; Samko, Stefan
A new subspace of Morrey spaces whose elements can be approximated by infinitely differentiable compactly supported functions is introduced. Consequently, we give an explicit description of the closure of the set of such functions in Morrey spaces. A generalisation of known embeddings of Morrey spaces into weighted Lebesgue spaces is also obtained. (C) 2016 Elsevier Inc. All rights reserved.
Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces
Publication . Almeida, Alexandre; Samko, Stefan
We prove that local generalized Morrey spaces are closely embedded between weighted Lebesgue spaces. We show that such embeddings are strict in all the cases under consideration by constructing counterexamples. As a consequence, continuous embeddings between generalized Morrey spaces and generalized Stummel spaces are established, as well as between Stummel classes (vanishing Stummel spaces). In particular, we obtain embeddings into a new Stummel class of functions with some vanishing property at infinity. We also partially improve a known result on the coincidence of Stummel spaces with a modification of Morrey spaces where the supremum norm is replaced by an integral L-p-norm. (C) 2017 Elsevier Ltd. All rights reserved.
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Fundação para a Ciência e a Tecnologia
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5876
Número da atribuição
UID/MAT/04106/2013